Methods for function approximation using Chebyshev Polynomials. These methods use
<a href="http://people.maths.ox.ac.uk/trefethen/publication/PDF/2004_106.pdf">Barycentric Interpolation</a>, 
which allows for efficient computation and numerical stability, even for high-order approximations. 
I use these approximations for solving ordinary differential equations and in the 
background of trajectory optimization problems.